Circle of illumination march equinox

Geography 100 online

Exercise #3: Earth-Sun Relationships and the Seasons (15 pts)

Earth-Sun relationships are important in understanding climate and weather patterns. Variations in the amount of solar energy at the earth's surface are a direct consequence of the earth's position and orientation in orbit. Variations in the angle of intercepted solar radiation, and differences in daylength are responsible for seasons.

1) Figure 1 is a view of the Earth in orbit looking down on the northern hemisphere. Match the correct letter in Figure 1 with each of these seasonal events (6 points):

aphelion

perihelion

vernal equinox

autumnal equinox

summer solstice

winter soltice

2) At what two points in the Earth’s orbit are daylengths the same at all latitudes? (1 point).

3) Which of the following latitudes experiences the longest period in the circle of illumination on January 1? (1 point)

36° S

18° N

35° N

63° N

Sun Angle

Because solar energy received by the earth follows essentially parallel pathways, and because the earth is spherical, at only one place on the earth’s surface can the sun’s rays strike vertically (this is known as the subsolar point). In other words, at only one place at any one time can the sun appear directly overhead. This occurs at solar noon when the sun reaches the highest position in the sky for that day. Because of the earth's limited axial tilt, the sun can appear directly overhead at the subsolar point at a relatively narrow range of latitudes over the course of a year (between 23.5° N and 23.5° S).

An important relationship exists between latitude and the angle of the noon sun. On the equinoxes (on March 21 or 22 and September 21 or 22) the sun’s rays are perpendicular to the earth at the equator. Those same rays would also be tangent at both of the poles, so that the sun would appear only on the horizon at those locations. On the same dates an observer at 30° N would record a sun angle of 60° above the southern horizon. Remember, the sun is 90° to the observer at the equator, minus the latitude of 30° (30° of arc) which equals 60°. This is called the angle of incidence, or sun angle. The angle of incidence decreases by 1° for every degree of arc of latitude between the observer's position and the location where the sun’s rays are vertical. This rule is the same for the other times of the year but is complicated by the earth's declination–the shift in angle when the sun's rays are not perpendicular to the equator. If the declination is 10° S, this means that the sun's rays are vertical at 10° S and an observer at 30° N would see the sun at 50° above the horizon 90-40 or 90-(30+10).

Use the formula:

angle of incidence = 90° - (latitude in degrees + declination in degrees*)

* If the declination is in the same hemisphere as the observer substract this.

Note: Keep in mind that solar noon is not the same as noon on our clock or watch because we are on standard time and typically daylight savings time. In the summer months in the U.S. solar noon is found around 1:00 pm.

4) For the locations listed below, calculate the solar noon sun angle (angle of incidence) for the following locations on the days listed (.5 points per angle, total of 3 points).

Note: Keep in mind you should know the sun’s declination for the solstices and equinoxes! If you cannot solve this, look at Figure 2 later in this exercise.

The sun's declination for October 20 = 10° S

May 15 = 19° N

April 15 = 9.5° N

Honolulu, Hawaii (19° N) on: May 15____

December 21____

Seattle, Washington (47° N) on: April 15____

October 20____

Nome, Alaska (65° N) on: December 21____

June 21____

Length of Daylight

Another factor in the spatial variation of insolation is length of daylight in a 24-hour period. Because of the Earth-Sun relationship and the spherical nature of the earth, low latitudes differ greatly from high latitude in the amount of time they spend in the circle of illumination. Examine the pattern of sunlight, latitude and time of year on Table 1.

Duration of Sunlight in the Northern Hemisphere

Table 1

Latitude

Northern Hem. Summer Solstice

Equinoxes

Northern Hem. Winter Solstice

90° N

24:00 hours

sun on horizon

0:00

80° N

24:00

12:00 hours

0:00

70° N

24:00

12:00

0:00

66.5° N

24:00

12:00

0:00

60° N

18:27

12:00

5:33

50° N

16:18

12:00

7:42

40° N

14:52

12:00

9:08

30° N

13:56

12:00

10:04

23.5° N

13:25

12:00

10:35

20° N

13:12

12:00

10:48

10° N

12:35

12:00

11:25

0°

12:06

12:00

11:54

5) Answer the following questions using Table 1.

a) What is the approximate daylength (time in the circle of illumination) for Cabo San Lucas, Mexico (23.5° N) on June 21? (1 point)

b) What is the approximate daylength (time in the circle of illumination) for Philadelphia, Pennsylvania (40° N) on December 21? Compare this with Oslo, Norway (60° N) on the same day. How much do they differ in hours and minutes? (3 points)

Spatial Patterns of Insolation

As one might expect, changing sun angle and daylength results in a distinct pattern of insolation by latitude over the course of a year. This pattern is shown in Figure 2. Figure 1 illustrates insolation levels, as measured in watts per square meter per day (watt/m2/day), at the top of the atmosphere.

Figure 2

image1.png

6) Answer the following questions using Figure 1.

a) How much does Seattle’s latitude receive in insolation on January 31, approximately? (1 point)

b) How much does Miami’s latitude receive in insolation on June 1, approximately? (1 point)

c) Which latitude receives the greatest variation in insolation over the course of a year? How much is this variation in watts/ m2/day? (2 points)